Yes, dogs can “have” wild squirrel. However, I think the pet food companies aren’t taking that exotic road just yet. It’s similiar to rabbit, which is already hard to find.
Dogs wouldn’t go out and specifically hunt squirrel; but if they decided to take a few bites of one, it won’t kill them. If your dog has a healthy immune system, they’ll survive through the rare intestinal parasite they may acquire. If you hunt it, deep freeze the squirrel meat (like you do any wild game meat) for at least 30 days to kill any parasites/larvae. You didn’t mention if you prepare it raw, dehydrated or cooked to your pet. You can make Kentucky Burgoo for them, stews make great toppers.
The proteins my pups got allergy tested for were as follows (no squirrel though!):
beef
buffalo
elk
goat
kangaroo
lamb
llama
pork/ham
rabbit
venison
yak
